Topic
Jaffard ring
About: Jaffard ring is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 3 citations.
Papers
TL;DR: In this article, the transfer of the strong S, catenarian, residually Jaffard and totally jaffard properties between the rings R(1) and R⟨1⟩ for domains R of dimension ǫ ≥ 2 was studied.
Abstract: The purpose of this paper is to find necessary and sufficient conditions for the transfer of the strong S, catenarian, residually Jaffard and totally Jaffard properties between the rings R(1) and R⟨1⟩ for domains R of dimension ≤ 2. Moreover, we give a positive answer to a conjecture of S. Kabbaj in the case of 2-dimensional integrally closed strong S-domains; we prove that if R is a 2-dimensional integrally closed strong S-domain then R[1] is catenarian.
3 citations
Journal Article•
TL;DR: In this article, the n-dimensional pair property was shown to transfer well in constructions involving pullbacks or passage to the associated reduced rings, but this property is not stable under passage to factor domains.
Abstract: If n is a nonnegative integer or infinity, and R is a (commutative unital) ring contained in a (commutative unital) ring T, then (R,T) is said to be an n-dimensional pair if every ring S that both contains R and is contained in T has Krull dimension n. For n greater than zero, examples are given of n-dimensional pairs that are not integral extensions, including an infinite family of examples that are neither LO-pairs nor INC-pairs. The n-dimensional pair property transfers well in constructions involving pullbacks or passage to the associated reduced rings, but this property is not stable under passage to factor domains. Special attention is paid to the n-dimensional pairs whose first coordinate is a Jaffard domain or a residually Jaffard ring. Also, examples are given of infinity-dimensional pairs whose intermediate rings have prime ideal chains of arbitrarily large cardinality; and of a family of n-dimensional pairs arising from minimal overrings.
1 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2007 | 1 |
| 2003 | 1 |